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Unformatted text preview: Math 182 Homework Section 6.5 Problem 12 A bucket that weighs 4lbs and a rope of negligible weight are used to draw water from a well that is 80 feet deep. The bucket is filled with 40lbs of water and is pulled up at a rate of 2 feet second . However, water leaks out of a hole in the bucket at a rate of . 2 lbs second . Find the work done in pulling the bucket to the top of the well. t seconds after the process begins we have that the height of the bucket is y = 2 t on the scale shown in the diagram. The weight of the bucket and water at this time is 4lbs and 40- . 2 t lbs respectively. Therefore, as a function of height y , the total weight of the bucket and water is (we replace t by y 2 ) to get 4 + 40- . 2 y 2 = 44- y 10 . The work required to move this bucket a tiny distance dy is thus (44- . 1 y ) dy . Therefore, the total work to raise the bucket is integraldisplay 80 (44- . 1 y ) dy = bracketleftbig 44 y- . 05 y 2 bracketrightbigvextendsingle vextendsingle y =80 y =0 = ( 44 · 80- . 05 · (80) 2 )- 0 = 3200 ft-lbs...
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